Theorem reccli

Description: Closure law for reciprocal. (Contributed by NM, 30-Apr-2005)

	Ref	Expression
Hypotheses	divclz.1	⊢ 𝐴 ∈ ℂ
	reccl.2	⊢ 𝐴 ≠ 0
Assertion	reccli	⊢ ( 1 / 𝐴 ) ∈ ℂ

Proof

Step	Hyp	Ref	Expression
1		divclz.1	⊢ 𝐴 ∈ ℂ
2		reccl.2	⊢ 𝐴 ≠ 0
3	1	recclzi	⊢ ( 𝐴 ≠ 0 → ( 1 / 𝐴 ) ∈ ℂ )
4	2 3	ax-mp	⊢ ( 1 / 𝐴 ) ∈ ℂ